Details

analyze763.0ms (15.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample39.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	201×	body	128	valid
7.0ms	256×	pre	128	true
5.0ms	19×	body	2048	valid
4.0ms	18×	body	1024	valid
3.0ms	10×	body	4096	valid
1.0ms	6×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify166.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.5b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.5b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
15.5b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_2773`
21×	`add-sqr-sqrt_binary64_2794`
20×	`add-cube-cbrt_binary64_2805`
18×	`times-frac_binary64_2779`
15×	`sqrt-prod_binary64_2788`
8×	`add-log-exp_binary64_2809`
6×	`add-exp-log_binary64_2808` `associate-/r*_binary64_2719` `add-cbrt-cube_binary64_2806`
5×	`pow1_binary64_2831`
4×	`sqrt-div_binary64_2789` `flip3-+_binary64_2776` `flip-+_binary64_2747`
3×	`associate-/l*_binary64_2720`
2×	`associate-/r/_binary64_2721` `sum-log_binary64_2861` `+-commutative_binary64_2705`
1×	`cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `div-inv_binary64_2770` `div-exp_binary64_2821` `distribute-lft-out_binary64_2726` `sqrt-pow1_binary64_2790` `clear-num_binary64_2772` `pow1/2_binary64_2850` `rem-sqrt-square_binary64_2786`

Counts

4 → 79

Calls

4 calls:

14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

series257.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
63.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
55.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
47.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4957	2082
1	4957	2082

prune342.0ms (6.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 11.3b

Counts

92 → 8

Compiler

Compiled 2492 to 1630 computations (34.6% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
4.5b	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
15.5b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.5b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite63.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_2794`
15×	`times-frac_binary64_2779` `*-un-lft-identity_binary64_2773`
9×	`add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806` `sqrt-prod_binary64_2788`
8×	`add-cube-cbrt_binary64_2805`
6×	`difference-of-squares_binary64_2742` `pow1_binary64_2831` `add-log-exp_binary64_2809`
4×	`sqrt-div_binary64_2789`
3×	`distribute-rgt-out--_binary64_2729` `flip3-+_binary64_2776` `associate-/r*_binary64_2719` `flip-+_binary64_2747`
2×	`cbrt-undiv_binary64_2804` `associate-/r/_binary64_2721` `div-exp_binary64_2821` `sqrt-pow1_binary64_2790` `pow1/2_binary64_2850` `rem-sqrt-square_binary64_2786`
1×	`cbrt-unprod_binary64_2803` `frac-2neg_binary64_2784` `diff-log_binary64_2862` `sub-neg_binary64_2766` `div-inv_binary64_2770` `flip3--_binary64_2777` `flip--_binary64_2748` `frac-sub_binary64_2782` `distribute-lft-out--_binary64_2727` `clear-num_binary64_2772` `prod-exp_binary64_2819` `associate-/l*_binary64_2720`

Counts

4 → 75

Calls

4 calls:

28.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
10.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series260.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
59.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
49.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
48.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify96.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4939	2399
1	4939	2399

prune219.0ms (4.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	87	8	95

Merged error: 11.3b

Counts

95 → 8

Compiler

Compiled 5026 to 3055 computations (39.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
5.4b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
15.5b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite51.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64_2794`
40×	`times-frac_binary64_2779`
36×	`*-un-lft-identity_binary64_2773`
34×	`add-cube-cbrt_binary64_2805`
26×	`sqrt-prod_binary64_2788`
24×	`associate-r_binary64_2715`
17×	`add-exp-log_binary64_2808`
11×	`add-cbrt-cube_binary64_2806`
9×	`pow1_binary64_2831`
6×	`sqrt-div_binary64_2789` `associate-/r*_binary64_2719` `add-log-exp_binary64_2809`
5×	`unswap-sqr_binary64_2741`
4×	`associate-/r/_binary64_2721` `flip3-+_binary64_2776` `div-exp_binary64_2821` `prod-exp_binary64_2819` `flip-+_binary64_2747`
3×	`pow-flip_binary64_2844` `associate-l_binary64_2716` `associate-/l*_binary64_2720`
2×	`cbrt-unprod_binary64_2803` `cbrt-undiv_binary64_2804` `div-inv_binary64_2770` `1-exp_binary64_2814` `sqrt-pow1_binary64_2790` `pow1/2_binary64_2850` `rec-exp_binary64_2820`
1×	`frac-2neg_binary64_2784` `pow-prod-down_binary64_2841` `sum-log_binary64_2861` `-commutative_binary64_2706` `clear-num_binary64_2772` `associate-r/_binary64_2717` `un-div-inv_binary64_2771` `+-commutative_binary64_2705` `inv-pow_binary64_2855` `rem-sqrt-square_binary64_2786`

Counts

4 → 122

Calls

4 calls:

19.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
3.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))

series247.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
66.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
56.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
47.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4940	2888
1	4940	2888

prune202.0ms (4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	131	11	142

Merged error: 11.3b

Counts

142 → 11

Compiler

Compiled 3848 to 2642 computations (31.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.2b	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
5.4b	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))
15.6b	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2794`
10×	`add-exp-log_binary64_2808`
9×	`add-cube-cbrt_binary64_2805` `*-un-lft-identity_binary64_2773`
8×	`add-log-exp_binary64_2809`
7×	`unpow-prod-down_binary64_2849` `associate-r_binary64_2715`
6×	`add-cbrt-cube_binary64_2806`
5×	`pow1_binary64_2831`
3×	`sqr-pow_binary64_2745` `unswap-sqr_binary64_2741` `pow-unpow_binary64_2847` `associate-l_binary64_2716` `prod-exp_binary64_2819`
2×	`pow-exp_binary64_2838` `pow-to-exp_binary64_2839` `flip3-+_binary64_2776` `sum-log_binary64_2861` `+-commutative_binary64_2705` `flip-+_binary64_2747`
1×	`cbrt-unprod_binary64_2803` `*-commutative_binary64_2706` `pow-pow_binary64_2842`

Counts

4 → 64

Calls

4 calls:

11.0ms	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
7.0ms	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)
6.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
4.0ms	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))

series327.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)
75.0ms	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))
66.0ms	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
39.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4912	1574
1	4912	1574

prune102.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	76	11	87

Merged error: 11.3b

Counts

87 → 11

Compiler

Compiled 1812 to 1229 computations (32.2% saved)

regimes63.0ms (1.3%)

Compiler: Compiled 764 to 558 computations (27% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	73
1	44	73

end0.0ms (0%)

sample1.5s (29.1%)

Algorithm

1×

intervals

Results

319.0ms	6106×	body	128	valid
206.0ms	767×	body	2048	valid
152.0ms	8000×	pre	128	true
103.0ms	509×	body	1024	valid
94.0ms	281×	body	4096	valid
33.0ms	221×	body	512	valid
11.0ms	116×	body	256	valid

Compiler

Compiled 464 to 339 computations (26.9% saved)

Details

analyze763.0ms (15.2%)

sample39.0ms (0.8%)

simplify166.0ms (3.3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite42.0ms (0.8%)

series257.0ms (5.1%)

simplify81.0ms (1.6%)

prune342.0ms (6.8%)

localize23.0ms (0.4%)

rewrite63.0ms (1.2%)

series260.0ms (5.2%)

simplify96.0ms (1.9%)

prune219.0ms (4.3%)

localize13.0ms (0.3%)

rewrite51.0ms (1%)

series247.0ms (4.9%)

simplify87.0ms (1.7%)

prune202.0ms (4%)

localize16.0ms (0.3%)

rewrite34.0ms (0.7%)

series327.0ms (6.5%)

simplify51.0ms (1%)

prune102.0ms (2%)

regimes63.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (29.1%)

Profiling